Melt a complex mesh and then animate it using force fields
For the melting you have lots of options, for example:


A high quality fluid simulation with a high viscosity. 
Shape keys + sculpting
Cast modifier (Apply as shape key)


The fluid simulation is probably the best for a good melting animation and being able to control it with force fields, but fluid simulations require tons of processing power to look good in my experience. I would probably go with casting it to a sphere with a &lt; 1 factor and a control object located slightly below the object. I'd apply that as a shape key and sculpt it a bit, and then only do the fluid sim when the object is already melted (there's less detail to lose when it's already smooth, and you might get away with lower settings.)